*Article* **Impact of Heat Generation on Magneto-Nanofluid Free Convection Flow about Sphere in the Plume Region**

### **Anwar Khan 1, Muhammad Ashraf 1, Ahmed M. Rashad 2 and Hossam A. Nabwey 3,4,\***


Received: 12 October 2020; Accepted: 9 November 2020; Published: 11 November 2020

**Abstract:** The main aim of the current study is to analyze the physical phenomenon of free convection nanofluids heat transfer along a sphere and fluid eruption through boundary layer into a plume region above the surface of the sphere. In the current study, the effect of heat generation with the inclusion of an applied magnetic field by considering nanofluids is incorporated. The dimensioned form of formulated equations of the said phenomenon is transformed into the non-dimensional form, and then solved numerically. The developed finite difference method along with the Thomas algorithm has been utilized to approximate the given equations. The numerical simulation is carried out for the different physical parameters involved, such as magnetic field parameter, Prandtl number, thermophoresis parameter, heat generation parameter, Schmidt number, and Brownian motion parameter. Later, the quantities, such as velocity, temperature, and mass distribution, are plotted under the impacts of different values of different controlling parameters to ascertain how these quantities are affected by these pertinent parameters. Moreover, the obtained results are displayed graphically as well in tabular form. The novelty of present work is that we first secure results around different points of a sphere and then the effects of all parameters are captured above the sphere in the plume.

**Keywords:** nanofluids; MHD; heat generation; sphere; plume; finite difference method
